Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
A polynomial characterization of some graph partitioning problems
Information Processing Letters
Journal of Combinatorial Theory Series B
Maximum cut on line and total graphs
Discrete Applied Mathematics
A characterization of weakly bipartite graphs
Journal of Combinatorial Theory Series B
A short proof of Guenin's characterization of weakly bipartite graphs
Journal of Combinatorial Theory Series B
On the complexity of the maximum cut problem
Nordic Journal of Computing
On the Complexity of the Maximum Cut Problem
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Complexity of Coloring Graphs without Forbidden Induced Subgraphs
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
On easy and hard hereditary classes of graphs with respect to the independent set problem
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Approximation algorithms for classes of graphs excluding single-crossing graphs as minors
Journal of Computer and System Sciences
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Note: MAX-CUT and MAX-BISECTION are NP-hard on unit disk graphs
Theoretical Computer Science
NP-hard graph problems and boundary classes of graphs
Theoretical Computer Science
Maximum independent sets in subclasses of P5-free graphs
Information Processing Letters
Note: max-cut and containment relations in graphs
Theoretical Computer Science
A characterisation of the complexity of forbidding subproblems in binary Max-CSP
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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We study MAX-CUT in classes of graphs defined by forbidding a single graph as a subgraph, induced subgraph, or minor. For the first two containment relations, we prove dichotomy theorems. For the minor order, we show how to solve MAX-CUT in polynomial time for the class obtained by forbidding a graph with crossing number at most one (this generalizes a known result for K5-minor-free graphs) and identify an open problem which is the missing case for a dichotomy theorem.